Polymers having conjugated double bonds, such as polyacetylene, have been known to form p-type or n-type conductive polyacetylene by electrochemically doping with anions such as ClO.sub.4.sup.-, PF.sub.6.sup.-, or BF.sub.4.sup.-, or with cations such as Li.sup.+ or (C.sub.4 H.sub.9).sub.4 N.sup.+ [J.C.S. Chem. Comm. (1979), pp. 594-595; C & EN, 26, 39 (1981)], and there have been disclosed chargeable cells utilizing the electrochemical doping. For example, a cell comprising positive and negative electrodes made of polyacetylene membrane and an organic electrolyte solution prepared by dissolving (C.sub.2 H.sub.9).sub.4 NClO.sub.4 in propylene carbonate can afford an open-circuit voltage of 2.5 V and a short-circuit current of 11.1 mA [J.C.S. Chem. Comm. (1981), pp. 317-319]. Recently, attention has been drawn to secondary cells having polyacetylene electrodes for their high energy density (Wh/kg) and high output density (W/kg). However, cells of this kind are quite defective in life, that is, they have a very short life in repeated charging and discharging and can hardly find practical use as secondary cells.